It is well known that pulsed Doppler radar systems have limits on unambiguous range and velocity, under which an increase in unambiguous velocity capability produces a decrease in unambiguous range capability, and vice versa. In practice this means that weather radars are unable to characterize the velocities present in severe weather events such as tornadoes. Methods to extend the unambiguous velocity range of weather radars include the use of multiple pulse-repetition frequencies, but such methods are unable to characterize the complex spectra encountered in tornadoes.